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    Piloting Hints & Tips
    From: Dan Hogan
    Date: 1998 Aug 19, 6:05 AM

    The following are a collection of piloting formulas and hints I have
    picked up over the years. I carry them in my Navigation Notebook. The
    "Distance Off Two Landmarks or Seamarks," was first shown to me by a
    friend that flew a TBM Avenger in WWII. He said 99% of his navigation
    to get back to the carrier was dead reckoning.
    
    =====================================================================
                    |First    | Second    |  Dist. Off    |   Dist. off
                    |Bearing  | Bearing   | Sec'd Bearing |     Abeam
    =====================================================================
    Bow & Bearing   |  45     |   90      | Dist. Run     | Dist. Run
    ---------------------------------------------------------------------
    Double Angle    |  ...    | 2 * First | Dist. Run     |
    ---------------------------------------------------------------------
    Seven Eights    |  30     |   60      | Dist. Run     |
    7/8(.875) *     |         |           |               |
    Dist Run        |         |           |               |
    ---------------------------------------------------------------------
    Seven Tenths    |  22.5   |   45      | Dist. Run     |
    7/10(0.7) *     |         |           |               |
    Dist Run        |         |           |               |
    ---------------------------------------------------------------------
    Prediction      |  26.5   |   45      | 1.4 * Dist Run|
    Dist. Run       |         |           |               |
    =====================================================================
    
    TIME/SPEED/DISTANCE ( In Hours, Knots, Nautical Miles)
    	Distance = Speed * Time * ((60, for minutes) or (3600, for
        seconds))
    
    THE RULE of 60
    	Distance Abeam * 60 = Bearing on the Bow * Range
    
    TIME at 1 Mile = 60 / Speed
    SPEED = (SQRT Bow Wave Length) * 1.33
    DISTANCE at 6 Minutes = 1/10 (0.1) * Speed
    
    DISTANCE TO HORIZON = 1.17 * SQRT of HE
    BREAKERS AT HORIZION = 3 Miles Off
    WINDOWS VISIBLE = 2 Miles Off
    COUNT TREES = 1 mile Off
    
    ECHO
      Distance Off = 1/2 Time in seconds * .18
    SOUND
      DISTANCE OFF = Time in Seconds * .18
    
    *************************
    
    FORMULAS FOR CALCULATORS
    	D = distance
    	R = distance run
    	A = First Bearing
    	B = Second Bearing
    
    Distance Off at Fiirst Bearing & Run Abeam
    	D = (R x sin A) / Cos A
    
    Distance Off Second Bearing Form Second Bearing on Bow & Run
    	D = (R x sin A) / (sin A [abs. diff.] B)
    
    Distance Off Abeam with Second Bearing on Bow and Run Betweeen
    	D1 = (R x sin 2B) / sin C
    	D2 = D1 x sin A (D2 = distance off abeam)
    
    Distance Run to a Given Bearing & Distance Off When on That Bearing
    	D1 = (R1 x sin B) / sin C
    	D2 = D1 x sin A (D2 equals distance off abeam)
    
    *************************************
    Sailing to Weather
    D = (200 / sine of the angle between tacks) * sine attack angle
    
    	D = percentage of the distance to the mark.
    	attack angle = the angle off the wind when sailing.
    
    *************************************
    Distance Off Two Landmarks or Seamarks
    	   s / SIN LS : a /sin LA : b / sin LB
    
    	s  = distance between marks
    	LS = angle diff between a & b
    	a  = distance from ship to b
    	LA = angle diff between bearing of a from ship & bearing of b from a
    	b  = distance from ship to a
    	LB = angle diff between bearing from b to a & Bearing b from ship
    
    ************************************
    Tacking Downwind
    
    Total distance sailed =
    2 * base distance * sin of the divergence angle/sin (divergence angle
    * 2)
    
    Chart:
    _____________________________________________________
    Divergence   |  Speed	 |  Distance	 |   Time
     angle       |	         |   to sail	 |   Hrs.
    -------------|-----------|---------------|-----------
                 |           |               |
    -------------|-----------|---------------|-----------
    
    
    
    Dan Hogan WA6PBY
    "Gacha" Catalina 27
    San Pedro, CA
    dhhogan{at}concentric.net
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